Let's say you're a day trader. You have X amount of dollars available total to invest. You get no money outside of this from any other sources, nor spend it on any other things than day-trading.
Because you're pretty good at what you do, you managed to actually extract some probabilistic knowledge about the future that is 100% accurate somehow.(don't ask how, you're just good at tarot)
You managed to do so for the following restricted set of stonks, that are independent(the numerical value of a piece of stonk is completely irrelevant, so all you know is what chance does it have to multiply it's value by an amount every day). We have an infinite amount of options for each stonk type(ie there are an infinite number of stonks of S1 type, of S2 type, etc...):
S1: 66% chance to half, 34% chance to double.
S2 0.1% chance to x10000, 99.9% chance to become 0
S3 48% chance to become 0, 52% chance to double
S4 80% chance to become 99%, 20% chance to become 105%
S5 20% chance to become 20% 50% chance to become 60% 15% chance to become 90% and 15% chance to become 140%
Let's do some math now. Suppose you invest Y amount of money in each of the stonks, what's your expected gain?
S1: 66% * 1/2 Y + 34% * 2 * Y = 101% Y
S2: 0.1% * 10000 Y + 99.1% * 0 = 1000% Y
S3: 48% * 0 + 52% * 2 Y = 104% Y
S4: 80% * 99% Y + 20% * 105 * Y = 100.2% Y
S5: 20% * 20% Y + 50% * 60% Y + 15% * 90% Y + 15% * 140% Y = 68.5% Y
Funnily enough, we can see stonk 5 is an extremely bad stonk to invest in, it's an actual loss of money.
Stonk 2 is an extremely profitable stonk to invest our money in theory, as it multiplies our investment tenfold on average!
Stonk 4, is a mild average profit of 0.2% per day
Stonk 3, a decent gain of 4% per day
Stonk 1, 1% per day.
Now. Obviously if we want the maximum amount of money like the greedy capitalists that we are, we want to invest as much as possible in stonks of the type 2. However. There comes a huge huge huge problem. How do we fucking do this?
If we go all in on stonk 2, bogdanoff will take all our money 999 out of 1000 times!
We simply cannot afford to go broke like that. 999 out of 1000 times, we're out of the game man. Wouldn't bet my life on that, would you?
Let's think about this in a different way. What if we take 2 stonks of type 2, and invest half and half in each?(no real reason to do it any differently since they're indistinguishable after all)
Well, now we have a 99.9% * 99.9% = 99.8001% chance of going broke!
Now, our maximum average profits have stayed the same, we still get 10x our investment on average. However! We only go broke 998 out of 1000 times!
Jeez man. We get one over Bogdanoff twice as often with this strategy. Which is pretty good, because Bogdanoff is a pretty evil man.
Ok, what happens if we divide our money into 10 stonks of type 2?
well, we will have a (99.9/100) to the power of 10 chances of ruin. that's only a 99.004488% chance of ruin!!!!
We're getting better at this, holy shit.
Ok let's go all in now. 1000 different stonks of type 2.
36% chance we go broke man. This is crazy. Bogdanoff is starting to get decimated.
What about 10000 stonks?
0.0045% chance of getting fucked over by Bogdanoff. Damn bro. This sounds like something I'd bet on this time around.
Clearly, given infinite stonk types, it's only rational to choose the most profitable one on average, and bet all our money spread out on many many different ones, this gives us both the highest possible return on investment and a infinitesimally low chance of ruin.
Now this is unrealistic, because there isn't an infinite supply of different stonks on the market. Damn. I can't be a broker yet I guess.
Well, I also don't wanna go broke man. So, while finding as many stonks of type 2 as I can, and evenly dividing my money into them is my most profitable action, it's simply not the action I should take most of the time.
suppose we limit ourselves to 1000 stonks of each type.
The most profitable strategy, is to still invest only in type 2, and well, one in 3 times I'm homeless I guess.
HOWEVER! man I just don't feel like going homeless, and getting less money per day is still acceptable, you know.
Here come in the other stonks to the rescue. And I leave figuring out a decent investment strategy to you ;)
